l/720th part of the zodiac circle, that is to say, h We do not know how he arrived at this pretty ace but, as he is credited with the invention of the ovc< have used this instrument for the purpose. Bui the discovery must apparently have been later th tise On dzes and distances, for the value of th angle is there assumed to be 2° (Hypothesis 6). tarchtis came to assume a value so excessive is un< the mathematics of his treatise is not dependent o value taken, 2° may have been assumed merely illustration; or it may have been a guess at tl diameter made before he had thought of attempt sure it. Aristarchus assumed that the angular < the sun and inoon at the centre of the earth are eq The method of the treatise depends on the just < which is Aristarchus's third ' hypothesis ', that' wh< appears to us halved, the great circle which divid and the bright portions of the moon is in the dire< eye*; the effect of this (since the moon receives its the sun), is that at the time of the dichotomy th the sun, moon and earth form a triangle right-an centre of the moon. Two other assumptions were first, an estimate of the size of the angle of the lat at the centre of the earth at the moment of dicho Anstarchus assumed (Hypothesis 4) to be 'less th rant by erne-thirtieth of a quadrant', i. e. 87° again rate estimate, the true value being 89° 50'; seoonc mate of the breadth of the earth's shadow where trmverses it: this he assumed to be 'the breac moons (Hypothesis 5).
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